If it is just a text file you can set 'cron' or 'at' (see man pages, or google for tutorials) to run a command like
mail -s "my backup" whoever@wherever < my_precious_file
at specified times. If the file is binary it seems like you can do a similar thing to send it as an attachment, but you need 'mutt' instead
mutt -a my_precious_file whoever@wherever
Ref:
http://mailman.u.washington.edu/pipe...er/005135.html